• Journal of the Korean Institute of Intelligent Systems
• /
• v.24 no.2
• /
• pp.201-208
• /
• 2014

Park et al. introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, we introduce new operations such as restricted union and restricted intersection and study their basic properties, and deal with the algebraic structure of generalized intuitionistic fuzzy soft sets. The lattice structures of generalized intuitionistic fuzzy soft sets are constructed.

• The Korean Journal of Applied Statistics
• /
• v.22 no.5
• /
• pp.1097-1102
• /
• 2009

Classification of subjects with unknown distribution in small sample size setup may involve order-restricted constraints in multivariate parameter setups. Those problems makes optimality of conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Redescending M-estimator along with that principle yields a considerably appropriate robust testing procedure. Furthermore, conditionally distribution-free test based upon exact permutation theory is used to generate p-values, even in small sample. Applications of this method are illustrated in simulated data and read data example (Lobenhofer et al., 2002)

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.331-347
• /
• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.

• Journal of Korean Institute of Industrial Engineers
• /
• v.10 no.2
• /
• pp.37-43
• /
• 1984

For the polymatroidal network, which has set-constraints on arcs, solution procedures to get the weighted maximal flows are investigated. These procedures are composed of the transformation of the polymatroidal network flow problem into a polymatroid intersection problem and a polymatroid intersection algorithm. A greedy polymatroid intersection algorithm is presented, and an example problem is solved. The greedy polymatroid intersection algorithm is a variation of Hassin's. According to these procedures, there is no need to convert the primal problem concerned into dual one. This differs from the procedures of Hassin, in which the dual restricted problem is used.

• The Korean Journal of Applied Statistics
• /
• v.24 no.1
• /
• pp.137-143
• /
• 2011

The classification of subjects with unknown distribution in a small sample size often involves order-restricted constraints in multivariate parameter setups. Those problems make the optimality of a conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Multivariate linear rank statistics along with that principle, yield a considerably appropriate robust testing procedure. Furthermore, conditionally distribution-free test based upon exact permutation theory is used to generate p-values, even in a small sample. Applications of this method are illustrated in a real microarray data example (Lobenhofer et al., 2002).

• Journal of the Korean Institute of Intelligent Systems
• /
• v.24 no.5
• /
• pp.569-577
• /
• 2014

Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with respect to some operations and the generalized intuitionistic fuzzy soft quotient algebra is established.

• Annals of Fuzzy Mathematics and Informatics
• /
• v.16 no.3
• /
• pp.261-284
• /
• 2018

In this paper, we recall the definition of soft set, fuzzy soft set, hesitant fuzzy set and hesitant fuzzy soft set and some of their examples. We define the concept of hesitant fuzzy soft multiset which combines hesitant fuzzy soft set and soft multiset theory. We also define basic terms in hesitant fuzzy soft multiset with relevant examples. Some basic operations such as restricted intersection, extended intersection, union, restricted union, AND-product and OR-product and their properties are given, supported with illustrative examples. We finally establish some important results, including De Morgan's inclusions and laws.

• Korean Journal of Mathematics
• /
• v.31 no.4
• /
• pp.465-477
• /
• 2023

In this paper, the concepts of soft PMS-algebras, soft PMS-subalgebras, soft PMS-ideals, and idealistic soft PMS-algebras are introduced, and their properties are studied. The restricted intersection, the extended intersection, union, AND operation, and the cartesian product of soft PMS-algebras, soft PMS-subalgebras, soft PMS-ideals, and idealistic soft PMS-algebras are established. Moreover, the homomorphic image and homomorphic pre-image of soft PMS-algebras are also studied.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2004.10a
• /
• pp.225-228
• /
• 2004

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We prove via the ellipsoid method the equivalence between the fully polynomial approximability and a certain pseudo-polynomial separability of the gknap polytope.

• Communications for Statistical Applications and Methods
• /
• v.25 no.5
• /
• pp.559-568
• /
• 2018

Gene classification can involve complex order-restricted inference. Examining gene expression pattern across groups with order-restriction makes standard statistical inference ineffective and thus, requires different methods. For this problem, Roy's union-intersection principle has some merit. The M-estimator adjusting for outlier arrays in a microarray study produces a robust test statistic with distribution-insensitive clustering of genes. The M-estimator in conjunction with a union-intersection principle provides a nonstandard robust procedure. By exact permutation distribution theory, a conditionally distribution-free test based on the proposed test statistic generates corresponding p-values in a small sample size setup. We apply a false discovery rate (FDR) as a multiple testing procedure to p-values in simulated data and real microarray data. FDR procedure for proposed test statistics controls the FDR at all levels of ${\alpha}$ and ${\pi}_0$ (the proportion of true null); however, the FDR procedure for test statistics based upon normal theory (ANOVA) fails to control FDR.